<snip>
The result I wish to achieve is to click on the icon for either GParted or
Synaptic *WITHOUT* being asked for a password (either root's or user's).
I've found vague hints that adding a line to my local /etc/sudoers file
such as
richard ALL = /usr/sbin/gparted , /usr/sbin/synaptic
would accomplish my goal.
Is that correct?
<snip>

I think that might work if clicking each icon actually runs those
commands from each .desktop file.

I believe it does:
1. if logged in as root, entering "/use/sbin/gparted" runs.
2. if *NOT* logged in as root, entering "/usr/sbin/gparted" asks
for password.

Yes, perhaps that's what sudo is for then (you'd have to run
"sudo /usr/sbin/gparted" instead: make it more convenient by
some wrapper [1]).
Of course the recommendation is still "don't do it", but the
good thing is: it's just that, a recommendation. FWIW, I went
through that phase and am back now to my "custom commands"
asking for a password when doing something sudo-ish. It's a
kind of "are you awake there, at the controls?"

That's what I want on all but one of my installs.

which I've come to appreciate. But to each her own and all that :-)
Cheers
[1] There are many solutions to that: I have a /home/tomas/bin
which I add to my PATH where I put all those little scripts
which are too small or too unstable to go to /usr/local/bin.
If I need a sudo in there, I just code it in. In my default
setting, I then get asked for a password. By relaxing sudoers
(e.g. with NOPASSWD: or !authenticate) you can fine tune that
to skip the authentication at a very fine-grained level (by
command, by user or by host (on which the command is running)).